Foundations of Physics

, Volume 34, Issue 9, pp 1431–1450 | Cite as

Fermi, Majorana and the Statistical Model of Atoms

  • E. Di Grezia
  • S. Esposito
Article

Abstract

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.

Thomas–Fermi model Majorana and the statistical atomic model exact and approximate solutions of the Thomas–Fermi equation atomic and molecular physics 

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REFERENCES

  1. 1.
    E. Fermi, "Sopra la teoria di Stern della costante assoluta dell 'entropia di un gas perfetto monoatomico, "Rend. Lincei 32, 395 (1923).Google Scholar
  2. 2.
    E. Fermi, "Considerazioni sulla quantizzazione dei sistemi che contengono degli elementi identici, "Nuovo Cim. 1, 45 (1924).Google Scholar
  3. 3.
    E. Fermi, "Sulla quantizzazione del gas perfetto monoatomico, "Rend. Lincei 3, 145 (1926). E. Fermi, "Zur Quantelung des Idealen Einatomigen Gases, "Z. Phys. 36, 902 (1926).Google Scholar
  4. 4.
    L. H. Thomas, "The calculation of atomic fields, "Proc. Cambr. Phil. Soc. 23, 542 (1926).Google Scholar
  5. 5.
    E. Fermi, "Un metodo statistico per la determinazione di alcune proprietá dell 'atomo, " Rend. Lincei 6, 602 (1927).Google Scholar
  6. 6.
    F. Rasetti in E. Fermi Collected Papers (Note e Memorie) (University of Chicago Press, Chicago, 1962) p. 277.Google Scholar
  7. 7.
    E. B. Baker, "The application of the Fermi-Thomas statistical model to the calculation of the potential distribution in positive ions, "Phys. Rev. 36, 630 (1930).Google Scholar
  8. 8.
    E. Guth and R. Peierls, "Application of the Fermi-Thomas model to positive ions, " Phys. Rev. 37, 217 (1931).Google Scholar
  9. 9.
    A. Sommerfeld, "Asymptotische integration der differentialgleichung des Thomas-Fermischen atoms, "Z. Phys. 78, 283 (1932).Google Scholar
  10. 10.
    E. Fermi, "Sulla deduzione statistica di alcune proprietá dell 'atomo. Calcolo della correzione di Rydberg per i termini S, "Rend. Lincei 7, 726 (1928).Google Scholar
  11. 11.
    E. Fermi, "¨Uber die anwendung der statistischen methode auf die probleme des atombaues, "Falkenhagen, Quantentheorie und Chemie, Leipziger Vortraege 95 (1928).Google Scholar
  12. 12.
    E. Whittaker and G. Robinson, The Calculus of Observations (Blackie, London, 1944), p. 365.Google Scholar
  13. 13.
    E. A. Milne, "The total energy of binding of a heavy atom, "Proc. Cambr. Phil. Soc. 23, 794 (1927).Google Scholar
  14. 14.
    E. Amaldi, "Ettore Majorana: Man and scientist, "in Strong and Weak Interactions. Present Problems, A. Zichichi, ed. (Acedemic, New York, 1966).Google Scholar
  15. 15.
    A. Sommerfeld, "Integrazione asintotica dell 'equazione differenziale di Thomas-Fermi, " Rend. Lincei 15, 788 (1932).Google Scholar
  16. 16.
    S. Esposito, "Majorana solution of the Thomas-Fermi equation, "Am. J. Phys. 70, 852 (2002).Google Scholar
  17. 17.
    E. Segré, Autobiogra a di un sico (Il Mulino, Bologna, 1995).Google Scholar
  18. 18.
    S. Esposito, E. Majorana Jr, A. van der Merwe and E. Recami eds., Ettore Majorana: Notes on Theoretical Physics (Kluwer Academic, New York, 2003).Google Scholar
  19. 19.
    S. L. Ross, Differential Equations (University of New Hampshire Blaisdell, Durham, 1964). G. Arfken. Mathematical Methods for Physicists (Academic, New York, 1970).Google Scholar
  20. 20.
    C. Miranda, "Teoremi e Metodi per l 'integrazione numerica della equazione differenziale di Fermi, "Rend. Reale Accademia d 'Italia 12, 286 (1934).Google Scholar
  21. 21.
    R. E. Marshak and H. A. Bethe, "The Generalized Thomas-Fermi Method as Applied to Stars, "Ap. J. 91, 239 (1940). H. A. Bethe, "Thomas-Fermi Theory of Nuclei, " Phys. Rev. 167, 879 (1968).Google Scholar
  22. 22.
    A. Mambriani, "Su una particolare equazione differenziale, "Rend. Lincei 9, 142 (1929).Google Scholar
  23. 23.
    G. Scorza-Dragoni, "A proposito di un 'equazione differenziale, "Rend. Lincei 8, 301 (1928); 9, 378 (1929).Google Scholar
  24. 24.
    R. P. Feynman, N. Metropolis, and E. Teller, "Equations of state of elements based on the generalized Fermi-Thomas theory, "Phys. Rev. 75, 1561 (1949).Google Scholar
  25. 25.
    E. Hille, "On the Thomas-Fermi equation, "Proc. N. A. S. 62, 7 (1969).Google Scholar
  26. 26.
    H. Lieb and B. Simon, "Thomas-Fermi theory of atoms, molecules and solids, "Adv.in Math. 23, 22 (1977).Google Scholar
  27. 27.
    F. Rasetti, "Eine statistische Berechnung der M-Röntgenterme, "Z. Phys. 48, 546 (1928).Google Scholar
  28. 28.
    G. Gentile and E. Majorana, "Sullo sdoppiamento dei termini Roentgen e ottici a causa dell 'elettrone rotante e sulle intensitá delle righe del cesio, "Rend. Lincei 8, 301 (1928);9, 229 (1928).Google Scholar
  29. 29.
    E. Fermi, "Sulla deduzione statistica di alcune proprietá dell 'atomo. Applicazione alla teoria del sistema periodico degli elementi, "Rend. Lincei 7, 342 (1928).Google Scholar
  30. 30.
    L. Spruch, "Pedagogic notes on the Thomas-Fermi theory (and on some improvements):atoms, stars and the stability of bulk matter, "Rev. Mod. Phys. 63, 151 (1991).Google Scholar
  31. 31.
    S. Esposito, "Majorana transformation for differential equations, "Int. J. Theor. Phys. 41, 2417 (2002).Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • E. Di Grezia
    • 1
    • 2
  • S. Esposito
    • 1
    • 2
    • 3
  1. 1.Dipartimento di Scienze FisicheUniversità di Napoli “Federico II” Complesso Universitario di Monte S. AngeloNapoliItaly
  2. 2.Istituto Nazionale di Fisica Nucleare, Sezione di NapoliComplesso Universitario di Monte S. AngeloNapoliItaly
  3. 3.Unità di Storia della Fisica, Facoltà di IngegneriaUniversità Statale di BergamoDalmine (BG)Italy

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